Question

if an object has zero Momentum does it have kinetic energy

Answer 1

If an object has zero momentum, then its kinetic energy is also zero.
Because the velocity is zero, it means that object is In the state of rest.

Answer 2

if the momentum is 0 that means that the m×v =0
as mass cannot be 0 that means that v=0 ,
$kinetic \: energy = \frac{1}{2} m {v}^{2}$
and here if v = 0 then ke is 0